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The enigma of the hiker

The enigma of the hiker

A hiker, very early in the morning, started climbing the path that leads to the mountaintop shelter. He does not walk with a regular pace but rather to contemplate the landscape, take pictures, rest, eat, so that he stops as soon as he accelerates or goes slowly. He reaches the top at sunset and after dinner he spends the night in the shelter. The next morning, when the dawn breaks, set off again, undoing the same path. It goes faster than the climb and by mid afternoon it has already reached the town.

Would you know if there is any point on the road where the hiker passes on each tour, at exactly the same time of day?

Solution

Yes there is a precise place on the road through which the hiker passes at exactly the same time in both days. To get a clear idea, imagine that at the same time that the hiker goes up, another one starts going down at the same time that he will do the next day and at the same pace that the hiker did on the way back, these two people would meet somewhere along the way and it is in this place where our hiker was at the same time in both days.